Nature (1876) Algorithm for Calculating the Date of Easter in the Gregorian Calendar

Originally published 1996 December by M.J. Montes.
This page was last updated 2001 July 31 by Marcos J. Montes.
The actual origin of this algorithm appears to be by an anonymous correspondent from New York to Nature in 1876 (Thanks Denis!). Samuel Butcher, Bishop of Meath, showed that this algorithm followed from Delambre's analytical solutions, and produces the date of Easter for all years. You can see the algorithm, as well as version for Orthodox Easter at another Easter Date site.

This algorithm appears in Practical Astronomy With Your Calculator, 2nd Edition by Peter Duffett-Smith, and he obtained this algorithm from Butcher's Ecclesiastical Calendar, published in 1876. This algorithm has also been published in the 1922 book General Astronomy by Spencer Jones; in The Journal of the British Astronomical Association (Vol.88, page 91, December 1977); and in Astronomical Algorithms (1991) by Jean Meeus.

This algorithm holds for any year in the Gregorian Calendar, which (of course) means years including and after 1583.

In the text below, / represents an integer division neglecting the remainder, while % is division keeping only the remainder. So 30/7=4 , and 30%7=2 .

        a=year%19
        b=year/100
        c=year%100
        d=b/4
        e=b%4
        f=(b+8)/25
        g=(b-f+1)/3
        h=(19*a+b-d-g+15)%30
        i=c/4
        k=c%4
        l=(32+2*e+2*i-h-k)%7
        m=(a+11*h+22*l)/451
        Easter Month =(h+l-7*m+114)/31  [3=March, 4=April]
        p=(h+l-7*m+114)%31
	Easter Date=p+1     (date in Easter Month)


References


Links

Oudin's Algorithm for the calculation of the date of Easter.
Carter's Algorithm for the calculation of the date of Easter.
Gauss' Algorithm for the calculation of the date of the Orthodox Easter.
Calculation of the Ecclesiastical Calendar
Last updated 2001 July 31.
Marcos J. Montes
mmontes@no.spam.smart.net